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Friday, June 20, 2008

Piano Notes and Exponential Frequencies



1) The C-notes on a piano double in frequency each time you move up one measure (7 white keys). This can be visually seen in the picture below by counting the amount of nodes on the sinousoidal wave ( i.e., ^v -> 2 nodes, ^v^v -> 4 nodes, ^v^v^v^v -> 8 nodes, etc.) for playing each C-note.

2) We could say the frequency has an exponential relationship, or that it doubles every 7 notes you go upscale (as in exponential growth) or that it halves for every 7 notes you go downscale (as in exponential decay)

3) The equation for this would be ...

... frequency = [some constant] x 2^(note / 7)


4) Whereby the notes in this example are defined as follows:

C4=0, D4=1, E4=2, F4=3, G4=4, A5=5, B5=6; then C5=7; C6=14; C7=21; etc... (just the number of notes from the bottom of the pictured keyboard, which happens to start at Middle-C or C4)

Therefore the frequency for C4 is 1, C5 is 2, C6 is 4, C7 is 8, C8 is 16, etc, times the constant 261.63 Hz (hertz). Or going downscale (not shown on picture), the frequency of C3 is 1/2, C2 is 1/4, and C1 is 1/8 times the constant 261.63 Hz.




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